What is Force and Pressure - It's Introduction, Their Types, Mathematical Expression, Examples

Force:

You are here because you probably want a clear, relatable analogy rather than a textbook definition. I should avoid technical language and focus on everyday experiences. Pushing a car seems like a good starting point, it's something most people have done. We can break it down into three key ideas: force as a push/pull, its connection to Newton's law, and how magnitude and direction matter.

The First Law tells us that a body at rest will remain at rest and a body in uniform motion will remain in uniform motion until it is compelled to change that state by a force impressed upon it. But what is a force? Think of force as a push or a pull. Every time you push a door open, pull a drawer, lift a bag, or kick a ball, you are applying a force. but we have to be more precise than that. Forces are not directly observable. What is perceived is the effect, the change produced by a force. In the beginning of the Principia, Newton defined force as “an action exerted upon a body, in order to change its state, either of rest or of moving uniformly. Force is the agent of change. In the particular case of dynamics, it is that which alters motion. It makes still things start moving, moving things speed up, slow down, stop, or change direction.

Force has Magnitude (strength) and Direction. You can't describe a force properly without both. Magnitude is how hard are you pushing. This is measured in Newtons (N). More mass, more force. Pushing a truck requires more force (newtons) than pushing a bike. Direction is where are you pushing? On left, right, up or down.

Mathematical expression:-

Now we should look at a mathematical explanation of force after the intuitive explanations. We start with Newton's second law for force since it's the most fundamental mathematical representation. We should avoid complex math but ensure the formulas are applied correctly.

Newton's Second Law of Motion,

F = m × a

· F is the force (N)
· m is the mass of an object (kg)
· a is the acceleration (m/s²)

This equation tells us two crucial things:

1. Force applied to an object is directly proportional to the acceleration it causes. To get twice the acceleration, you need to apply twice the force.

2. The acceleration is inversely proportional to the mass. The more mass an object has, the more force is required to change its velocity. Because force causes acceleration, force is also a vector quantity.

Example Calculation: You push a 20 kg box so it accelerates at 4 m/s².How much force did you apply?

· F = m × a
· F = 20 kg × 4 m/s²
· F = 80 kg⋅m/s² = 20 N

Force at atomic level:-

Now we will study atomic-level explanation of force after already getting intuitive and mathematical definitions. The key is to connect macroscopic experiences like pushing and pulling to microscopic interactions between atoms. Imagine force is a push or a pull between atoms. All forces we experience macroscopically like pushing a wall are the sum of all the invisible electromagnetic pushes between the atoms of two objects. No physical touch is actually required at the atomic level just close enough interaction for these electromagnetic fields to exert influence.

e.g. - When you push on a wall, the atoms in your hand get extremely close to the atoms on the wall's surface. The negatively charged electron clouds of these atoms repel each other. This electromagnetic repulsion is the force you feel. Your hand doesn't go through the wall because of this repulsive force. When you pull on a string, the atoms in the string are being pulled apart. The electromagnetic bonds between them act like microscopic springs. The force you feel is the combined resistance of all these tiny springs wanting to snap back to their original length.

Types of forces:-

Now we will see an intuitive explanation of different types of forces, building on previous discussions about force. Let's break down the different types of forces we experience in the universe. We can categorize them into two main groups: Fundamental Forces and Everyday Forces.

There are four fundamental forces: gravitational, electromagnetic, strong, and weak. They are basic building blocks of all interactions in the universe. Every push or pull you've ever experienced is ultimately due to one of these four.

1. Gravity:

An attractive force between any two objects that have mass. The bigger the masses, the stronger the pull. The farther apart they are, the weaker the pull. The force weakens a lot with distance. It pulls stuff together. Always. It never pushes. We will understand by experiments. Think of space as a stretched rubber sheet. A heavy ball like a star would make a deep dent. A marble like a planet rolling nearby would fall into that dent, orbiting around the heavy ball. Gravity is the effect of mass warping space itself.

e.g. The Earth is so massive that its gravity pulls everything like you, your phone, the atmosphere toward its center, giving things weight. The Moon's gravity pulls on the Earth's oceans, causing tides.

2. Electromagnetism:

It attracts opposite charges and repels same charges. It's the reason we never truly "touch" anything at the atomic level, it's the repulsion between electron clouds that we feel as a solid surface. Think of magnets. The invisible pull between a north and south pole is electromagnetism. The invisible push between two north poles is also electromagnetism.

e.g. It's the force behind almost everything in daily life. It holds atoms together to form molecules. It creates friction, tension, and the normal force. It is responsible for light, electricity, and magnetism.

3. Strong Nuclear Force:

The super glue of the universe. Protons are all positively charged and should violently repel each other due to electromagnetism. The strong force is an incredibly powerful, short-range glue that overcomes this repulsion and binds protons and neutrons together. Without it, atomic nuclei wouldn't exist except for hydrogen. There would be no atoms, no elements, no universe as we know it.

e.g. Imagine a tiny, tiny capsule where you've trapped several incredibly strong magnets all trying to push each other apart. The capsule itself is the strong force it's the only thing strong enough to keep them all locked together.

4. Weak Nuclear Force:

Responsible for radioactive decay. The process that changes one type of subatomic particle into another. It's the force that allows neutrons to turn into protons and vice versa, which is a key process in how stars burn and in radioactive elements like uranium breaking down.

e.g. imagine a busy club with two rooms: a proton room and a neutron room. The weak force is the bouncer that occasionally lets a particle change its identity and switch rooms.

There are five everyday forces: normal, friction, tension, spring force, drag. They are not fundamental; they are the results of the electromagnetic force playing out in different scenarios. These forces require touching, they also known as Contact Forces.

1. Normal Force:

The normal force is nothing but push back from surface. When an object presses against a surface, the surface pushes back with exactly enough force to prevent the object from passing through it. It's always perpendicular to the surface.

e.g. A cat sits on a table. Gravity pulls the cat down. The table pushes back up with an equal force. That upward push is the normal force. If you lean against a wall, the wall pushes back on you.

2. Friction:

Friction is grip. The things eventually stop because of friction. The force that opposes motion between two surfaces that are in contact. At the atomic level, even surfaces that look smooth are rough. As they slide against each other, atoms bump and their electron clouds repel. This interaction creates resistance.

Friction have two types:

1. Static Friction:

Static friction prevents motion. Static is is stronger and happens before movement. It's the force that prevents motion from starting. Imagine you're trying to push a very heavy box across the floor. It will not move until you push hard enough to move it. It's the initial resistance you feel when you start pushing. The box doesn't move. When you push and it pushes back. When you push a little harder, and it pushes back a little harder. That's static friction increasing to match you. At certain point, Static friction matches your pushing force exactly. Once your push exceeds this maximum force, the box starts to move.

2. Kinetic Friction:

Kinetic friction resists motion. Kinetic is weaker and happens during movement. It's the force that opposes motion that has already started. It's not trying to stop it from happening; it's just making it difficult to keep going. Once the box is moving, this is the force that acts against its motion, causing it to eventually stop. Let's take example of box. Once the box starts moving, The resistance you feel is now constant and less than the maximum push you needed to start moving. This constant drag is kinetic friction. You still have to push to keep it going. If you stop pushing, kinetic friction is what brings the box to a stop.

3. Tension:

The pulling force transmitted through a string, rope, cable, or chain when it is pulled tight from opposite ends. Tension is pulling force. A rope, string, or cable can only pull; it can never push. Always acts away from the object along the rope. Therefore, on any free-body diagram, the tension force is always drawn directed away from the object, along the line of the rope. If the rope is pulling the box to the right.Therefore, on the box's FBD, you draw a force vector (T) pointing away from the box, to the right.

e.g. A dog on a leash. The dog pulls one way, you pull the other. The leash is in tension, and that force is what you feel in your hand and what the dog feels on its collar.

4. Spring Force:

The force exerted by a compressed or stretched spring. The more you deform it, the harder it pushes or pulls back. e.g. The bounce of a trampoline, the shock absorber in your car, or the feeling of pushing a pin into a cushion.

Just like tension, the force vector is drawn pointing away from the object you are analyzing, along the spring's axis, because it is pulling on that object. Because when you pull on the spring, lengthening it. It wants to return to its relaxed length. To return to its relaxed state, it pulls inward.

e.g. A spring is attached to a wall and a box. You pull the box to the right, stretching the spring.

On the box's FBD: The spring force points left toward the wall. The spring is pulling the box back to the left.
On the wall's FBD: The spring force points right (toward the box). The spring is pulling the wall to the right.

But that doesn't happen when you push on the spring to shortening it. That time It also wants to return to its relaxed length. But to return to its relaxed state, it pushes outward. The force vector is drawn pointing away from the object you are analyzing, along the spring's axis, because it is pushing on that object.

e.g. You push a box against a spring mounted on a wall, compressing it.

On the box's FBD: The spring force points right away from the wall. The spring is pushing the box away to the right.
On the wall's FBD: The spring force points left away from the box. The spring is pushing the wall to the left.

5. Air Resistance (Drag):

A special type of friction that objects experience as they move through the air. The air molecules constantly collide with the object, slowing it down. Think of it as the air fighting back against an object moving through it. It's a force that purely opposes motion.
e.g. The reason a piece of paper flutters to the ground instead of falling straight down like a rock. Stick your hand out of a moving car window. The push you feel back against your hand is air resistance. A parachute works by maximizing this force.

Air resistance always acts in the opposite direction to the object's motion relative to the air. Identify the Direction of Motion. What way is the object moving. On your FBD,draw the air resistance force vector pointing directly opposite to the direction of motion.

Imagine car driving on road, it moves to right. The air pushes back against the front of the car. The force vector points left.
A skydiver falling downwards Air pushes up against his body. The force vector points upward.

Pressure:

Pressure is a force applied perpendicular to the surface of an object per unit area. It’s not just about how hard you push, but also about how small or big the point of contact is. The same force can cause low pressure or high pressure, depending on the area it's spread over. The best way to understand pressure is through examples you already know. You need to use a lot of force to cut a tomato when knife has a wider edge, because the pressure isn't very high. When you apply the same amount of force by knife which has an incredibly fine edge. It's pressure is all concentrated on that minuscule point, creating immense pressure that slices through the tomato easily. Unlike force, standard pressure is a scalar quantity. It has a magnitude but no specific direction. At a specific point in a fluid, pressure acts equally in all directions, which is why it's treated as a scalar.

Mathematical expression:-

Now we should look at a mathematical
explanation of force after the intuitive explanations. Pressure is defined as the amount of force applied perpendicularly to a surface per unit of area over which that force is distributed.

The Formula, P = F / A

· P is the pressure (Pascals, Pa) (1 Pa = 1 N/m²).
· F is the normal force (N)
· A is the area over which the force is distributed (m²)

What this equation tells us that:

1. Pressure is inversely proportional to Area. For constant force, if you decrease the area (A), the pressure (P) increases. This explains why a sharp knife with small area cuts better than a dull one with larger area with the same force.

2. Pressure is proportional to force: For a constant area, if you increase the force (F), the pressure (P) increases.

e.g. A woman weighing 80N wears high heels. One heel has an area of 2 m². What is the pressure she exerts when all her weight is on one heel?

· P = F / A
· P = 80 N / 2 m²
· P = 40 N/m² = 40 Pa

Pressure at atomic level:-

Now we will study atomic-level explanation of pressure after already getting intuitive and mathematical definitions. For pressure, imagine how many atomic collisions over an area create the net effect we perceive as pressure. Now, let's think about gases and liquids which are easier to visualize for pressure. Imagine a closed container of gas. The gas inside is made of molecules flying around at incredible speeds, bouncing off each other and the sides of the containerr. Every single time one of these molecules strikes the wall of the container, it gives a force to the wall. Pressure is the total force from all these billions of collisions divided by the area of the wall. It's the average intensity of this microscopic hailstorm.

If you pump more gas into the container, there are more molecules to hit the wall each second. Which means more collisions per second causes higher pressure. If you heat the gas, the molecules move faster. They hit the wall harder and they hit more often. Which increase the total force on the wall, and therefore the pressure. If you keep the same number of molecules but make the container bigger, the same number of collisions are now spread out over a larger space. The force per unit area decreases.

Types of pressure:-

Now we will see an intuitive explanation of different types of pressures, building on previous discussions about pressure. The type of pressure just tells us what we're using as a reference point for measurement. It's like describing how high a building is: do you measure from ground level, or from the first floor?

There are four types of pressures: absolute pressure, gauge pressure, differential pressure and partial pressure.

1. Absolute Pressure:

This is the total, actual pressure starting from a perfect vacuum. Vacuum is empty space with zero atoms. Absolute zero pressure is the starting point. It is always positive. You can't have less than zero pressure. The air pressure around us is actually absolute pressure. The total weight of the entire atmosphere pressing down on us is 14.7 pounds per square inch (PSI) at sea level, measured from the vacuum of space.

You take a deflated balloon. It looks like it has zero pressure. But it doesn't! The miles of air above us is constantly pressing down on it with a force of about 14.7 pounds per square inch (psi). This is the Absolute Pressure inside and outside the balloon. Because it's equal, the balloon doesn't inflate. When you start blowing air into the balloon. You are adding more air molecules inside the balloon. They bounce around and push outward on the balloon's inside. The pressure inside the balloon is now the Absolute Pressure (atmospheric pressure + the extra pressure from your breath). While the pressure outside is still just the atmospheric pressure.

The Simple Relationship: Absolute Pressure = Atmospheric Pressure + Gauge Pressure

2. Gauge Pressure:

This is the pressure above the atmospheric pressure around us. It ignores the ever present air pressure and only measures the extra. Measuring the height of a mountain from sea level. We don't care about the distance from the Earth's core, we just care about how much it sticks up above the water.

When we blow a balloon. The air which makes ballon expand is difference between absolute pressure and atmospheric pressure. This difference is called Gauge Pressure.

It can be positive or negative. When absolute pressure is higher than the atmosphere like full tire or a balloon, then gauge pressure is positive. When absolute pressure is lower than the atmosphere like sipping a drink through a straw, a vacuum cleaner hose, then gauge pressure is positive.

e.g. This is what your car tire gauge measures. When it reads 32 PSI, it means the pressure inside the tire is 32 PSI more than the air pressure outside the tire which is 14.7 PSI. The absolute pressure inside the tire is actually 32 + 14.7 = 46.7 PSI.

3. Differential Pressure:

Differential pressure is simply the difference in pressure between two points. It doesn't care what the absolute or gauge values are, only the gap between them.

In balanced pressure or no differential, nothing happens. In unbalanced pressure or differential, one side is higher. This imbalance causes air, water or any fluid to roll downhill from the high-pressure side to the low-pressure side. Differential pressure is the pressure hill that makes fluids flow. No hill, no flow. A bigger hill means faster flow. It’s one of the most useful concepts in engineering and physics.

Imagine you're in a house with all the windows and doors closed. The air pressure is equal everywhere. Now, you open a single front door. The pressure inside and outside is almost equal. There is very little differential pressure across the door. The air doesn't rush in or out. The door just sits there. On windy day, the wind creates a high-pressure zone outside. The pressure on the outside of the door is now higher than the pressure on the inside. A differential pressure exists. Air forcefully rushes into the house through the door, from high pressure to low pressure. You might even feel the door try to push open. You Turn on a Giant Exhaust Fan in house. The fan sucks air out of the house, creating a low pressure zone inside. The pressure on the inside of the door is now lower than the pressure on the outside. A differential pressure exists again. Air rushes into the house from outside, from high to low. This is exactly how a vacuum cleaner works. In both windy scenarios, it was the difference in pressure between the two sides of the door that caused air to move.

Then how it's measured. It has two ports. One port connects to point A. The other port connects to point B. The gauge simply measures A minus B and shows you the difference.

e.g.
1. A fan works by creating a zone of high pressure behind it and low pressure in front of it. The differential pressure is what makes the air move from high to low.
2. Differential pressure is what makes airplane fly. The shape of the wing forces air moving over the top to travel faster than air moving underneath. According to Bernoulli's principle, fast moving fluid has lower pressure. This creates a differential pressure. Higher pressure on the bottom of the wing and lower pressure on the top. This Differential pressure is the primary source of lift. The high pressure pushes the wing and the plane up toward the low-pressure zone. The pilot controls this differential pressure with the plane's speed and the angle of the wing.

4. Partial Pressure:

In a mixture of gases, each gas contributes a part of the total pressure. This individual contribution is its partial pressure. Each gas in a mixture behaves as if it were alone in the container. Think of it like this, If you could magically remove every other gas from the room, the pressure left behind from the one remaining gas would be its partial pressure.

Imagine a mixture of gases (like air) as a crowd of different people (oxygen molecules, nitrogen molecules, CO₂ molecules, etc.). Total Pressure is The force from the entire crowd pushing on a surface. Partial Pressure is the force from just one group in that crowd (e.g., just the oxygen molecules) pushing on that same surface. Each gas in a mixture behaves as if it alone occupied the entire volume. Its partial pressure is the pressure it would exert if all other gases were removed.

Many biological and chemical processes don't care about the total pressure; they only care about the pressure of the specific gas they interact with.

e.g. 1. The air we breathe is 78% Nitrogen and 21% Oxygen. The total absolute pressure is 14.7 PSI. The partial pressure of Oxygen is 21% of that, or about 3.1 PSI. This is the value that actually matters for our lungs to absorb oxygen into our blood.

2. It is used in packaging. The air inside potato chip bags is not normal air. It's often almost pure Nitrogen (N₂). Oxygen causes spoilage (oxidizes fats, helps microbes grow). By removing oxygen, its partial pressure inside the bag is nearly zero. The inert nitrogen provides the cushioning and prevents the chips from being crushed, while the lack of oxygen keeps them fresh.